# Find parent of given node in a Binary Tree with given postorder traversal

Given two integers N and K where N denotes the height of a binary tree, the task is to find the parent of the node with value K in a binary tree whose postorder traversal is first natural numbers .

For N = 3, the Tree will be -

7
/   \
3     6
/   \  /  \
1     2 4   5


Examples:

Input: N = 4, K = 5
Output: 6
Explanation:
Parent of the node 5 is 6. As shown in the tree above.

Input: N = 5, K = 3
Output: 7
Explanation:
Parent of the node 3 is 7. As shown in the tree above.

Naive Approach: A simple approach is to build the tree according to the following pattern and then traverse the whole tree to find the parent of a given node.

Efficient Approach: The idea is to use binary search to find the parent of the node. As we know the binary Tree of Height N has nodes. Therefore, the search space for the binary search will be 1 to . Now each node has children value either or . Therefore, parent of such node can be found easily.

Below is the implementation of the above approach:

## C++

 // C++ implementation to find the  // parent of the given node K in  // a binary tree whose post-order  // traversal is N natural numbers     #include  using namespace std;     // Function to find the parent  // of the given node  int findParent(int height, int node)  {      int start = 1;      int end = pow(2, height) - 1;         // Condition to check whether      // the given node is a root node.      // if it is then return -1 because      // root node has no parent      if (end == node)          return -1;         // Loop till we found      // the given node      while (node >= 1) {          end = end - 1;             // Finding the middle node of the          // tree because at every level          // tree parent is          // divided into two halves          int mid = start                    + (end - start)                          / 2;             // if the node is found return          // the parent always the child          // nodes of every node          // is node/2 or (node-1)          if (mid == node || end == node) {              return (end + 1);          }             // if the node to be found          // is greater than the mid          // search for left subtree else          // search in right subtree          else if (node < mid) {              end = mid;          }          else {              start = mid;          }      }  }     // Driver Code  int main()  {      int height = 4;      int node = 6;         int k = findParent(height, node);      cout << k;         return 0;  }

## Python

 # Python implementation to find the  # parent of the given node     import math      # Function to find the parent   # of the given node  def findParent(height, node):         start = 1     end = pow(2, height) - 1        # Check whether the given node       # is a root node.if it is then       # return -1 because root       # node has no parent      if (end == node):          return -1        # Loop till we found       # the given node      while(node >= 1):             end = end - 1            # Find the middle node of the           # tree because at every level           # tree parent is divided           # into two halves          mid = start + (end - start)//2            # if the node is found           # return the parent          # always the child nodes of every          # node is node / 2 or (node-1)           if(mid == node or end == node):              return (end + 1)                     # if the node to be found is greater          # than the mid search for left          # subtree else search in right subtree          elif (node < mid):              end = mid             else:              start = mid     # Driver code  if __name__ == "__main__":      height = 4     node = 6            # Function Call      k = findParent(height, node)      print(k)

Output:

7


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